Logarithmic number systems (LNS) offer a viable alternative in terms of area, delay, and power to binary number systems for implementing multiplication and division operations for applications in signal processing. The Mitchell algorithm (MA), proposed in [15], reduces the complexity of finding the logarithms and the antilogarithms using piecewise straight line approximations of the logarithm and the antilogarithm curves. The approximations, however, result in some loss of accuracy. Thus, several methods have been proposed in the literature for improving the accuracy of Mitchell's algorithm. In this work, we investigate a new method based on Operand Decomposition (OD) to improve the accuracy of Mitchell's algorithm when applied to logarithmic multiplication. In the OD technique proposed in [9] for reducing the amount of switching activity in binary multiplication, the two inputs to be multiplied are together decomposed into four binary operands and the product is expressed as the sum of the products of the decomposed numbers. We show that applying operand decomposition to the inputs as a preprocessing step to Mitchell's multiplication algorithm significantly improves the accuracy. Experimental results indicate that the proposed algorithm for logarithmic multiplication reduces the error percentage of Mitchell's algorithm by 44.7 percent on the average. It is also shown that the OD method yields further improvement when combined with the other correction methods proposed in the literature.